I see no reason why any difficulty along this line arises in the first place.
In my model all evolving universes have rules of state succession that
allow some degree of true noise entering the universe at each transition.
In this venue there would be an infinite number of universes that have
rules with low randomness in large and medium [many many bits] "events",
substantial randomness in moderately small [moderate number of bits]
"events", and a sharp roll off in the number of the very smallest [one bit]
This seems a decent description of universes like ours and there would be
an infinite number of them. The same number as for any style of universe.